How to factor y2 plus y-2?

Answer 1

y2+y-2 factors to (y+2)(y-1)

The two initial terms of your factoring (y and y) must multiply to equal the first term of your starting problem (y2). Likewise, the last two terms must multiply to equal the last term of your starting problem (-1 * 2 = -2).

You know that one way to reach y2 by multiplying two terms is doing y*y, so your first terms are most likely each y. There are two possible ways of multiplying two terms to equal -2, (2* -1) and (-2 * 1). To decide which version to use, look at the middle term of the starting problem. The coefficient on the middle term must result from adding the two factors that will multiply to equal your third term. That is to say, for this problem, the correct combination of multiplying to equal -2 must add together to equal 1. If we used -2 and 1, these terms add together to equal -1, not 1. If we use the other combination, we get a sum of 1, so this is the correct combination. You simply mate the first terms you determined (y and y) with the second terms you determined (2 and -1).

This leaves: (y+2)(y-1).

Note: If no solution exists for the above method, it is likely a non-factorable trinomial, which will require the use of the quadratic formula.